This invention relates to a three-dimensional model displaying method of displaying on a display screen a three-dimensional model expressed in a computer in the field of CAD or CAM.
Recently, computer graphics have remarkably advanced with improvement of hardware and software in computer technique. A technique for describing a three-dimensional model (three-dimensional model) as well as a two-dimensional model (planar model) has advanced from a wire frame method in which only the contour of an object is drawn to a solid method in which the surface of an object is described.
The display of a three-dimensional model with shading image has been disclosed in detail by the publications "Principles of Interactive Computer Graphics", "W.H. Newman & R.F. Sproull, McGRAW-HILL 1981", "Fundamentals of Interactive Computer Graphics", and "J.D. Foley & A. VAN DAM, Addison Wesley, 1982". In this connection, a method is generally employed in which the surface of a three-dimensional model is divided (or sampled) into triangular patches, quadrangular patches or polygonal patches, of which a value normal to each path is obtained by using the outer products of the sides thereof. The color of the patch is determined according to the normal, and the triangular, rectangular or polygonal region projected on the screen is painted in the color thus determined. The method will be described with reference to the ordinary case where the surface is divided into quadrangular patches. First, the surface of a three-dimensional model is divided into a number of quadrangular patches, and the normal vector of each quadrangular patch is obtained. Thereafter, the luminance of the patch is obtained according to the normal vector. The four vertexes P.sub.i,j, P.sub.i+1,j, P.sub.i+1,j+1 and P.sub.i,j+1 of the quadrangular patch are coordinate- transformed into four points Q.sub.i,j, Q.sub.i+1,j, Q.sub.i+1,j+1, and Q.sub.i,j+1 in a two-dimensional coordinate system on the display screen, respectively. Thereafter, the region defined by the four points Q.sub.i,j, Q.sub.i+1,j, Q.sub.i+1,j+1, and Q.sub.i,j+1 is painted with predetermined color and luminance. The above-described operation is carried out for all of the quadrangular patches forming the surface of the three-dimensional model, thus displaying the latter with shading image. Removal of the hidden surface can be achieved by controlling the quadrangular patch processing sequence.
The conventional three-dimensional model describing method as described above suffers from the following difficulties: In order to display a three-dimensional model with shading image, it is necessary to paint each quadrangular patch whose sides form different angles with the coordinate axes on the display screen. Therefore, in the case where the number of sampling points (or the number of quadrangular patches) is large, a heavy load is applied to the computer, and accordingly the processing speed is lowered.
The processing speed may be increased by decreasing the number of times of painting; i.e., by reducing the number of sampling points. However, this will induce another difficulty that the description of the three-dimensional model is lower in accuracy.